We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux function, in which the traffic density and the headway are the averaged quantities. A numerical study illustrates the performance of the second order model compared to the particle approach. We also analyse numerically uncertain traffic accidents by considering statistical measures of the solution to the PDEs.
Hydrodynamic traffic flow models including random accidents: A kinetic derivation / Chiarello, Felisia Angela; Göttlich, Simone; Schillinger, Thomas; Tosin, Andrea. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 22:3(2024), pp. 845-870. [10.4310/CMS.2024.v22.n3.a10]
Hydrodynamic traffic flow models including random accidents: A kinetic derivation
Tosin, Andrea
2024
Abstract
We present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux function, in which the traffic density and the headway are the averaged quantities. A numerical study illustrates the performance of the second order model compared to the particle approach. We also analyse numerically uncertain traffic accidents by considering statistical measures of the solution to the PDEs.File | Dimensione | Formato | |
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CfaGsStTa-uncertain_accidents.pdf
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chiarello2024CMS.pdf
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https://hdl.handle.net/11583/2985821